Tag Info

Based upon what you have written (including comments)
You are a visa national from Nigeria who applied for entry clearance
as a visitor
You did not include supporting documents to show your financial
status
You did not explain why you previously stayed in the UK significantly
beyond the intention you stated in a previous application
You used an alias ...

Yes you can apply for a visa while you are in Switzerland. As per the official Tourist/Business visa page for US embassy in Switzerland there is nothing to prohibits you from doing so.
However, you will need a list of documents that might not be available with you:
Current proof of income, tax payments, property or business ownership, or assets, ...

Yes. While you are meant to apply for a visa to your main, intended destination country, it doesn't really matter that much once you get your visa. There's nothing to stop you changing your mind about where you go when you get to Schengen. You can travel freely within the Schengen Area and leave from wherever you like. Once you leave Schengen (in your case ...

Hungary is part of the Schengen area, so you'll need a Schengen visa to visit (assuming you're not already in a Schengen area country, in that case you can travel without a visa). If you intend to study there, you should apply for a student visa.
UK is outside of the Schengen zone, so your immigration status there is not relevant. However, being deported ...

There isn't a passport check to get out of the country.
The airline will generally check your passport to make sure you have permission to enter the destination (they have to bear the cost of returning you if you are refused entry) and the staff at security and boarding will normally check some form of Id matches your ticket - but mostly to make sure you ...

Of course. A visa is merely a statement of period of validity - you're asking the country for permission to enter between dates x and y.
If you also need permission for dates y to z, or different dates entirely, you can do so.
Depending on the country, reason for second visa, and type of visa, they may either allow you to have two valid visas in your ...

Yes you should be able to get another UK visa without any issues.
Of course you must make sure that you don't violate any other visa conditions. As mentioned by @DumbCoder, UK specifically stops pregnant women, becuse they can give birth in UK and then demand UK residency because of the child